Answer: choice D 1/2
Step-by-step explanation:
Events A and B are independent if the equation P(A∩B) = P(A) · P(B) holds true.
so
1/6=1/3*p(A)
p(A)=1/2
Answer:
Bushel
Step-by-step explanation:
The Difference Between a Bushel and a Peck
Both are a dry volume measure of quarts. A bushel is equal to 32 quarts, while a peck is equal to 8 quarts, or a quarter of a bushel.
Answer:
The surface area is equal to ![390\ in^{2}](https://tex.z-dn.net/?f=390%5C%20in%5E%7B2%7D)
Step-by-step explanation:
The surface area of the triangular pyramid is equal to the area of its four triangular faces
so
In this problem
![SA=4[\frac{1}{2}(b)(h)]](https://tex.z-dn.net/?f=SA%3D4%5B%5Cfrac%7B1%7D%7B2%7D%28b%29%28h%29%5D)
we have
![b=15\ in](https://tex.z-dn.net/?f=b%3D15%5C%20in)
![h=13\ in](https://tex.z-dn.net/?f=h%3D13%5C%20in)
substitute the values
![SA=4[\frac{1}{2}(15)(13)]=390\ in^{2}](https://tex.z-dn.net/?f=SA%3D4%5B%5Cfrac%7B1%7D%7B2%7D%2815%29%2813%29%5D%3D390%5C%20in%5E%7B2%7D)
Answer:
Where can I find specific information on Florida driving laws? Visit the official Florida driver's handbook page to find all of the driving laws and information you need to know for the Class E knowledge exam.
Step-by-step explanation:
Answer:
Using either method, we obtain: ![t^\frac{3}{8}](https://tex.z-dn.net/?f=t%5E%5Cfrac%7B3%7D%7B8%7D)
Step-by-step explanation:
a) By evaluating the integral:
![\frac{d}{dt} \int\limits^t_0 {\sqrt[8]{u^3} } \, du](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdt%7D%20%5Cint%5Climits%5Et_0%20%7B%5Csqrt%5B8%5D%7Bu%5E3%7D%20%7D%20%5C%2C%20du)
The integral itself can be evaluated by writing the root and exponent of the variable u as: ![\sqrt[8]{u^3} =u^{\frac{3}{8}](https://tex.z-dn.net/?f=%5Csqrt%5B8%5D%7Bu%5E3%7D%20%3Du%5E%7B%5Cfrac%7B3%7D%7B8%7D)
Then, an antiderivative of this is: ![\frac{8}{11} u^\frac{3+8}{8} =\frac{8}{11} u^\frac{11}{8}](https://tex.z-dn.net/?f=%5Cfrac%7B8%7D%7B11%7D%20u%5E%5Cfrac%7B3%2B8%7D%7B8%7D%20%3D%5Cfrac%7B8%7D%7B11%7D%20u%5E%5Cfrac%7B11%7D%7B8%7D)
which evaluated between the limits of integration gives:
![\frac{8}{11} t^\frac{11}{8}-\frac{8}{11} 0^\frac{11}{8}=\frac{8}{11} t^\frac{11}{8}](https://tex.z-dn.net/?f=%5Cfrac%7B8%7D%7B11%7D%20t%5E%5Cfrac%7B11%7D%7B8%7D-%5Cfrac%7B8%7D%7B11%7D%200%5E%5Cfrac%7B11%7D%7B8%7D%3D%5Cfrac%7B8%7D%7B11%7D%20t%5E%5Cfrac%7B11%7D%7B8%7D)
and now the derivative of this expression with respect to "t" is:
![\frac{d}{dt} (\frac{8}{11} t^\frac{11}{8})=\frac{8}{11}\,*\,\frac{11}{8}\,t^\frac{3}{8}=t^\frac{3}{8}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdt%7D%20%28%5Cfrac%7B8%7D%7B11%7D%20t%5E%5Cfrac%7B11%7D%7B8%7D%29%3D%5Cfrac%7B8%7D%7B11%7D%5C%2C%2A%5C%2C%5Cfrac%7B11%7D%7B8%7D%5C%2Ct%5E%5Cfrac%7B3%7D%7B8%7D%3Dt%5E%5Cfrac%7B3%7D%7B8%7D)
b) by differentiating the integral directly: We use Part 1 of the Fundamental Theorem of Calculus which states:
"If f is continuous on [a,b] then
![g(x)=\int\limits^x_a {f(t)} \, dt](https://tex.z-dn.net/?f=g%28x%29%3D%5Cint%5Climits%5Ex_a%20%7Bf%28t%29%7D%20%5C%2C%20dt)
is continuous on [a,b], differentiable on (a,b) and ![g'(x)=f(x)](https://tex.z-dn.net/?f=g%27%28x%29%3Df%28x%29)
Since this this function
is continuous starting at zero, and differentiable on values larger than zero, then we can apply the theorem. That means:
![\frac{d}{dt} \int\limits^t_0 {u^\frac{3}{8} } } \, du=t^\frac{3}{8}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdt%7D%20%5Cint%5Climits%5Et_0%20%7Bu%5E%5Cfrac%7B3%7D%7B8%7D%20%7D%20%7D%20%5C%2C%20du%3Dt%5E%5Cfrac%7B3%7D%7B8%7D)